Magnetic recording devices such as magnetic disk drives are widely used for storing digital data. In such devices, the data is typically stored on the surface of moving magnetic media such as rigid or flexible magnetic disks, magnetic tapes or magnetic drums. Data is generally recorded on such magnetic media in magnetic recording tracks which extends generally linearly along the surface of the media.
The track width of a magnetic recording system at which the storage capacity is maximized has been estimated.
T. Howell and E. Feig, IEEE International Symposium of Information Theory, Ann-Arbor, Mich., Oct 6-9, 1986; PA1 J. C. Mallinson, IEEE Trans. Magn., vol. MAG-10, pp. 368-373, (June 1974); PA1 D. F. Eldridge, IEEE Trans. Audio., vol. AU-11, pp. 3-6, January-February 1963. PA1 J. C. Mallinson, Proceedings IEEE, (February 1976); M. Wildmann, IEEE Trans. Magn., vol. MAG-10, pp. 509-514, (September 1974). PA1 1) A. Peled and A. Ruiz, Proc, IEEE International Conference on Acoustics, Speech, and Signal Processing, Denver Colo. pp. 964-967; (April 1980), PA1 2) F. Mintzer and T. Howell, OBM-RC 9429 (#41644), (16 Jun. 1982); PA1 3) E. Feig and F. Mintzer, IBM-RC 13701 (#60788), (14 Mar. 988); and PA1 4) S. B. Weinstein and P. M. Ebert, IEEE Trans. Comm., vol. COM-19, pp. 628-634, (October, 1971).
The approach was to apply Shannon's formula for the information capacity of a communications channel C. E. Shannon, Bell Syst. Tech. J. 27, pp. 623-656, (October 1958) It was concluded in line with an information theoretical tenet that "a plethora of low-performance channels has a greater capacity than a single channel of high performance." In these earlier works, the noise power in the channel was assumed to depend linearly on the track width. This is a property of media noise, which was assumed there to be the fundamental limitation in recording. Signal power, on the other hand, grows quadratically with track width. These earlier works concluded that storage capacity is fundamentally a monotonically increasing function of track density.
In a more recent study electronic noise was added to the analysis. T. Howell and E. Feig, IEEE International Symposium of Information Theory, Ann-Arbor, Mich., Oct 6-9, 1986; Electronic noise is characterized by being essentially constant, effectively independent of track width. Optimality was no longer achieved assymptotically by increasing arbitrarily track density. Instead, capacity first peaked and then dropped assymptotically to zero as the number of tracks was increased. The problem of interference from neighboring tracks was not considered.
A major contributor to signal degradation in conventional magnetic recording devices is interference from neighboring tracks due to imperfect servo mechanics. Neighboring track interference becomes critical as tracks become narrower, because then the ratio of the interfering signal to desired signal increases. Moreover, the power of the interfering signal also grows quadratically with the width of that portion of the head which slides over it. Mallinson has stated that "it is safe to conclude that purely mechanical limitations, primarily related to the difficulty of keeping the reproduce head on track while in the reproduce mode, will impose more stringent ultimate limitations than those associated with purely electrical or magnetic phenomena."
The analysis of the Howell and Feig presentation can be extended to incorporating the servo issue into the model. The resulting analysis gives a qualitative picture of the effects on channel capacity of the various contributing noise sources. It is assumed that the servo mechanics are such that the deviations from center track are random, Gaussian with zero mean and variance .sigma..sup.2. The magnetic recording head width is allowed to be narrower that the track width. With the usual read/write methods, the principle of "write wide-read narrow" seems justifiable, as far as channel capacity is concerned. Channel capacity is increased if narrower tracks are used. However, the ratio of head-width to track-width to achieves maximum capacity decreases with decreasing values of track-width until an optimal head-width/track-width combination is obtained, after which the ratio increases asymptotically to one. The initial drop in ratio arises in part because the interfering signals from the neighboring tracks become more and more significant as the tracks get narrower.
Writing narrower tracks tends to introduce "dead regions" which yield signals which are faulty over some significant interval of time. With wide tracks, faulty media spots are but a speck with respect the rest of the media defining the track width. These specks become more and more damaging as tracks get narrower.